FUND.OF PHYSICS(LL)-PRINT COMP-W/ACCESS
FUND.OF PHYSICS(LL)-PRINT COMP-W/ACCESS
11th Edition
ISBN: 9781119455608
Author: Halliday
Publisher: WILEY
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Chapter 11, Problem 1Q

Figure 11-23 shows three particles of the same mass and the same constant speed moving as indicated by the velocity vectors. Points a, b, c, and d form a square, with point e at the center. Rank the points according to the magnitude of the net angular momentum of the three-particle system when measured about the points, greatest first.

Chapter 11, Problem 1Q, Figure 11-23 shows three particles of the same mass and the same constant speed moving as indicated

Figure 11-23 Question 1.

Expert Solution & Answer
Check Mark
To determine

To find:

Ranking the points according to the magnitude of the net angular momentum of the three-particle system.

Answer to Problem 1Q

Solution:

Ranking of magnitude of net angular momentum is

La>Lb=Lc>Le>Ld

Explanation of Solution

1) Concept:

We can use the concept of angular momentum to find the net angular momentum about each point given.

2) Formulae:

L = r×mv

3) Given:

Three masses and their velocity vectors are given.

4) Calculations:

Angular momentum about any point is,

L = r×mv

We can write magnitude as,

L= rmvsinθ

Where, L is angular momentum, r is position vector,v is velocity vector, θ is angle between  r  and v. We can write r for rsinθ .

So, we can write ,

L=rmv.

 The angular momentum is positive for counter clockwise direction and negative for clockwise direction.

Calculation for net angular momentum about point a:

Let l is the side of square.

La=mv0+mvl+mvl

La=2mvl

Calculation for net angular momentum about point b:

Lb=mv0+mv0+mvl

Lb=mvl

Calculation for net angular momentum about point c:

Lc=-mvl+mv0+mv0

Lc=-mvl

Calculation for net angular momentum about point d:

Ld=mvl+-mvl+mv0

Ld=0

Calculation for net angular momentum about point e:

Le=-mvl2+mvl2+mvl2

Le=mvl2

Ranking of magnitude of angular momentum is:

La>Lb=Lc>Le>Ld

Conclusion:

We can rank magnitude of net angular momentum using angular momentum concept. We can write equation for each point given at corners of the square.

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Chapter 11 Solutions

FUND.OF PHYSICS(LL)-PRINT COMP-W/ACCESS

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